Characterizing twin-particle entanglement in double-well potentials

We consider a pair of twin atoms trapped in double-well potentials. For each atom, two orthogonal spatial modes are accessible: the states $|L\rangle$ and $|R\rangle$ spatially localized in the left and right wells respectively. Furthermore the twin atoms are distinguishable thanks to an additional degree of freedom. We propose a method for experimentally quantifying the particle entanglement between these atoms which allows us to probe a violation of Bell's inequality. It is based on measuring the correlations in the atoms' momentum distribution. If the tunneling and the energy difference between the wells are tunable, then full state tomography is achievable.